problem 223 mathcounts

Mathematics
Tutor: None Selected Time limit: 1 Day

In a basketball league of n teams in which each team plays every other team twice, the total number of games played is n^2-n. How many teams are in the league if 56 games were played?

Sep 21st, 2014

n^2-n=56

n^2-n-56=0

n^2-8n+7n-56=0

n(n-8)+7(n-8)=0

(n-8)(n+7)=0

n=8 or n=-7 

n= -7 is not admissible.

Hence there are 8 teams


Sep 21st, 2014

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